Differential Geometry Seminar: Aspherical Complex Surfaces

The collection of manifolds is vast and diverse. One class that we can hope to understand are those which have contractible universal cover, namely aspherical manifolds. These manifolds are determined up to homotopy equivalence by their fundamental group.

There are several conjectures related to the Euler characteristic and signature of aspherical manifolds, namely the Hopf conjecture, the Singer conjecture, and in dimension 4, the Gromov-Luck inequality. We discuss these conjectures in the setting of aspherical complex surfaces. This is joint work with Luca Di Cerbo and Luigi Lombardi.

School of Computer and Mathematical Sciences